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$E$-$g$-frames

H. Hedayatirad, T. L. Shateri

Abstract

In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study some prperties of $E$-$g$-frames. First, we give a result concerning perturbation of $E$-$g$-frames and then use it to construct $E$-$g$-frames in separable Hilbert spaces.

$E$-$g$-frames

Abstract

In the present paper, we introduce the notion of --frames for a separable Hilbert spaces , where is an invertible infinite matrix mapping on the Hilbert space . We study some prperties of --frames. First, we give a result concerning perturbation of --frames and then use it to construct --frames in separable Hilbert spaces.
Paper Structure (2 sections, 10 theorems, 38 equations)

This paper contains 2 sections, 10 theorems, 38 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. $E$-$g$-frames

Key Result

Proposition 2.4

Let $\Lambda=\{\Lambda_n\}_{n\in\mathbb N}$ be an $E$-$g$-frame with frame bounds $A$ and $B$. Then the $E$-$g$-frame operator $S_{\Lambda}$ is bounded, invertible, self-adjoint, and positive and $A\leq S_{\Lambda}\leq B$.

Theorems & Definitions (21)

  • Definition 1.1
  • Definition 2.1
  • Example 2.2
  • Example 2.3
  • Proposition 2.4
  • Remark 2.5
  • Proposition 2.6
  • proof
  • Remark 2.7
  • Theorem 2.8
  • ...and 11 more